A New York rental application is a legal document that allows a landlord to review a potential tenant's background information and references. Use the forms below to start or answer an eviction lawsuit where the landlord is claiming that the tenant owes back rent.Once you have found your new home, you will be asked to fill out a rental application form. The applicant will need to sign the application form and associated certifications agreeing that the information provided in the application is accurate. Landlord and Tenant matters are brought in District Court, where you can sue for housing problems and evictions. How to fill out the New York Rental Application Form? 1. Gather all required documents and personal information. 2. A New York lease agreement is a binding contract that allows a landlord to rent residential or commercial space to a tenant in exchange for payment. A Rental Registration Form must be filed whenever a change in rental occupancy occurs. Garden City, NY 11530.